In this thesis, the main approach to the characterization of the
set of classical probabilities, the correlation polytope approach,
is reviewed for different scenarios, namely, hidden variable models
discussed by Bell (local), Kochen and Specker (non-contextual), and
Leggett and Garg (macrorealist). Computational difficulties
associated with the method are described and a method to overcome
them in several nontrivial cases is presented. For the quantum
case, a general method to analyze quantum correlations in the
sequential measurement scenario is provided, which allows
computation of the maximal correlations. Such a method has a direct
application for computation of maximal quantum violations of
Leggett-Garg inequalities and it is relevant in the analysis of
non-contextuality tests. Finally, possible applications of the
results for quantum information tasks are discussed.
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